You are correct.
Besides Woodruff's mention in his book there are a couple of mentions in letters of Union Soldiers which mention watching her burn. They described her as being reconstructed as and Ironclad with railroad rails stacked on her decks. I'll bet a lot of that iron is still at the bottom of the Arkansas River unless it was dregged up when they dug the present day navigation channel.
She would have been ineffectual as an ironclad, because she already was heavy in the water drawing 11 feet for her keel. The Corp of Engineers only maintains a present day navigation channel of only 15 feet. She would have had to wait until flood season to have navigated the Arkansas River below Pine Bluff to the Mississippi in 1863.
Woodruff would have had an intimate knowledge of the Ponchartrain because at the time of the fall of Little Rock the last remaining two guns from the Ponchartrain were assigned to his command. They had been moved from Fort Pleasent (near Pine Bluff) to be installed as part of the defences at Little Rock, but were never emplaced and were captured by Gen Steele's army sitting in the old Little Rock Arsenal.
Steele had no use for these guns so he ordered them thrown into the Arkansas River very near when the Ponchartrain had burned. After the war during the Brooks/Baxter conflict during reconstruction, Woodruff salvaged these two guns and used them in that little piece of history.
One of those two guns still sits on the old State House Museum Lawn in Little Rock today. The other, a 9 inch naval gun, was lost during the 1927 flood that washed away most of Arkansas Post where in had been moved in 1920 as a memorial to the Battle of Arkansas Post.
I understand that the Arkansas Naval Museum is planning to rebuild a large scale model of the CSS Arkansas for display. Maybe a monument to the CSS Ponchartrain would be in order also since it is the only "Known" navy vessel sunk on that site.